What happens to the power on the raspberry pi 3 when I do a shutdown from the "Raspbian GUI" or the command line?
The Raspberry Pi cannot turn itself off properly. Thats why after a Raspbian shutdown the Pi will still consume an non-negligble amount of current (up to 30 mA). This also means that the 5V rail is indeed always on.
You can soft reboot your Pi with
And your Pi will continue to consume power if plugged in and shutdown.
If you want a hard reboot, just disconnect the power (after shutting down) and reconnect.